r/g — The Return on Capital vs. Growth

r is the return on capital and g is the growth rate of the economy. Piketty’s claim is r > g: wealth grows faster than income, so capital concentrates. It may be the most disputed argument in modern economic theory, and it is disputed from both directions at once. One side reads “r > g, therefore social control” (a global wealth tax); the other reads “it depends, therefore the free market.” This page treats the ratio as the contested variable, not a settled conclusion. The finding: almost nobody disputes that r has historically exceeded g. Piketty himself calls it “a historical fact, not a logical necessity.” The fight is over conditions the inequality says nothing about: does r hold up as capital piles up, do fortunes compound or dissipate, and what does r actually measure? Neither policy inference follows from the ratio. Both ride on the conditions. And by 2015 Piketty himself had narrowed r > g to one tool among several, not the primary explanation.

Links: Economics, The Supply Omission (g decomposed: output = labor × productivity), Inflation (the Cantillon transfer: how wealth shifts “without notice”), Productivity–Pay Gap (capital vs. labor share, gross vs. net), Positional Goods (housing, the one capital share that grew), Inequality Optimum (the normative layer: how much concentration is functional), Taxation and Unrealized Gains (what a wealth tax would actually tax)

Neutral by design (Chris: “I would rather the page be neutral”). Both sides are grounded to equal depth. Source-checked 2026-10-01 against primary texts; sources are listed at the bottom. Chris: “this will also be a learning exercise for me as I obviously don’t have the details correct either.” §6 records what the check corrected, his details and mine both.

1. What the ratio claims, mechanically

A fortune that earns r and is fully reinvested grows at r. The economy, and the labor income inside it, grows at g. So the fortune’s size relative to the economy grows at roughly r − g. Piketty frames this with two “fundamental laws”:

First law: α = r × β. Capital’s share of income (α) equals the return on capital times the capital/income ratio (β). This is an accounting identity (Capital, ch. 1).
Second law: β = s / g. In the long run, the capital/income ratio tends to the net saving rate divided by growth (Capital, ch. 5). This is a steady-state tendency, not an identity: slow growth with steady saving means a rising β. Income here is net of depreciation.

Piketty’s historical claim (Capital ch. 10, pp. 353–356): from antiquity to the 17th century, g “never exceeded 0.1–0.2 percent for long.” The pure return on capital, by contrast, centered on 4–5%, so r was “at least 10 to 20 times greater” than g. Here r is the pretax pure return: net of management costs and excluding capital gains and losses. The 20th-century reversal was “a concatenation of circumstances”: wartime destruction, progressive taxation made possible by the shocks of 1914–1945, and exceptional postwar growth (world g of 3.5–4% from 1950 to 2012). After taxes and war losses, net r fell to roughly 1–1.5% in 1913–1950, below g. The gap “will widen again” as growth, “especially demographic growth,” slows.

2. The case that r > g drives concentration

The long US series. Saez & Zucman (2016): the top 0.1% wealth share rose “from 7% in 1978 to 22% in 2012, a level almost as high as in 1929.”
Large fortunes earn higher r.
- Piketty’s endowment table (Capital Table 12.2): real returns from 1980 to 2010 were 10.2% for Harvard/Yale/Princeton, 8.8% for endowments over $1bn, and 6.2% for those under $100m. (These include capital gains from the falling-rate window; see §4.)
- Stronger, independent evidence: Fagereng, Guiso, Malacrino & Pistaferri (2020), using Norwegian registry data, find returns rise with wealth (about 18 points from the 10th to the 90th percentile, about 10 net of tax). They also find returns are persistent and correlated across generations.
The shift toward shareholders is partly real. Greenwald, Lettau & Ludvigson (2025) attribute 40% of US equity value growth from 1989 to 2017 to “reallocation of rewards to shareholders … primarily at the expense of labor compensation.”
“It’s housing” moves the concentration, it doesn’t refute it. Piketty’s 2015 reply accepts a multi-sector, relative-price story (real estate, energy). Housing is still wealth.
Policy conclusion drawn: a progressive global tax on capital (Capital ch. 15). His illustrative schedule is 0% below €1m, 1% from €1m to €5m, and 2% above €5m, with possibly 5–10% on the largest fortunes. He calls it a “useful utopia.” In 2015 he wrote that stabilizing concentration might need top rates “as large as 5 percent per year, and possibly higher.”

3. The case that “it depends”

Diminishing returns: the net-σ objection. As β rises, r should fall. Piketty’s mechanism needs the net elasticity of substitution between capital and labor to exceed 1. Summers (2014): “I know of no study suggesting that measuring output in net terms, the elasticity of substitution is greater than 1.” Rognlie (2015) makes the same point: gross elasticity always exceeds net, and of 31 estimates surveyed, “only 5 show a gross elasticity above 1, and only 2 imply a net elasticity above 1.” Rising r − g “requires even more unlikely levels of substitutability.” (In 2015 Piketty said σ > 1 “is not my favored interpretation.”)
Housing. Net of depreciation, the rise in capital’s share since 1948 “comes entirely from the housing sector; the contribution … from all other sectors has been zero or slightly negative” (Rognlie 2015). Read against Piketty, this says the mechanism is one asset class, not capital in general. (What drives housing is a separate question. Chris: “I don’t want to attribute housing too much to zoning, as these trends seem more macro”: the rise looks cross-country and rate-linked, not a local land-use story.)
The second law overstates the effect. Krusell & Smith (2015): Piketty holds the net saving rate fixed, which implies a gross saving rate heading to 100% as g → 0. A fixed gross rate “is much to be preferred,” and with it, halving g raises the capital/income ratio only modestly.
Fortunes dissipate. Summers (2014): every $1 of wealth raises spending by about 5 cents, “just enough to offset the accumulation.” And “less than one tenth of the 1982 [Forbes 400] list was still on the list in 2012,” although most would have stayed on with a plain 4% real return. Arnott, Bernstein & Wu (2015) say the same: spending, charity, taxes and splitting among heirs erode dynasties. This is the measured form of “shirtsleeves to shirtsleeves in three generations.”
No cross-country signal. Acemoglu & Robinson (2015): general laws “ignore the central role of political and economic institutions.” In a panel from 1870, they find “no evidence of a positive impact of r−g on top inequality.” Using bond-rate measures, the sign is often negative.
Lower top shares under other methods. Smith, Zidar & Zwick (2023) put the top 0.1% at 15.7% in 2016, not ~22%, by allowing returns to vary within asset classes.
Not pure compounding even in the friendly data. Saez & Zucman attribute the rise to “the upsurge of top incomes combined with an increase in saving rate inequality.” The new top holders are younger and earn more of the economy’s labor income.
Piketty’s own narrowing (AER 2015): “I do not view r > g as the only or even the primary tool for considering changes in income and wealth in the twentieth century, or for forecasting the path of inequality in the twenty-first century.” On top labor income specifically, the rise “has evidently little to do with r − g.”
Policy conclusion drawn: the conditions, not the ratio, decide outcomes. Competition, diminishing returns and dissipation erode r without a wealth tax.

4. What r measures: the discount-rate problem

Piketty’s r excludes capital gains. But the measured wealth surge after 1980, including the endowment returns in §2, includes them. Part of those gains came from falling interest rates: price ≈ earnings ÷ (discount rate − growth), so a lower discount rate raises every asset’s price at once.

How much? Greenwald, Lettau & Ludvigson (2025) decompose real US equity growth of 7.2% a year (1989–2017):

Source	Share
Shift of income from labor to shareholders	40%
Economic growth	25%
Lower price of risk	21%
Lower interest rates	14%

So the discount-rate channel is roughly a third. It is real, but it is not the bulk. The largest piece is a genuine shift of cash flows toward capital, which is §2’s strongest point. Gomez & Gouin-Bonenfant (2024) find falling rates explain about 40% of the rise in top-wealth inequality. Their mechanism runs mainly through entrepreneurs raising cheap capital, not passive holders being revalued.

Chris: “Inflation is the mechanism for wealth transfer without ‘notice’, and it is a key factor” (the Cantillon channel). The literature supports “key factor” at about a third to two-fifths. The rest is not an artifact.

5. Where the dispute actually lives

The disagreement is in the rows, not in the ratio. “r > g, therefore control” and “it depends, therefore markets” both skip from the ratio to a policy without arguing the rows. And the ratio’s own author treats it as one input rather than the engine.

6. What the source check corrected (the learning record)

g before industrialization was 0.1–0.2%, not “~1%.” The gap was an order of magnitude larger than I had it.
Piketty’s r excludes capital gains. So the post-1980 revaluation argument is mostly aimed at measured wealth, not at his r.
The rate-revaluation share was overstated. I had written “a large part, with no change in underlying cash flows.” Measured, it is about a third, and the largest piece is a real shift from labor to capital. This partly trims Chris’s concession too: rates are a key factor, not the main one.
Piketty’s 2015 narrowing is broader than “not top labor income.” He denies r > g is even the primary tool for the 20th century.
The σ objection is about the net elasticity, and Summers made it before Rognlie.
Chetty is probably not an r/g story (see the specimen). Chetty’s decomposition is about how growth was shared: restoring the 1940 distribution closes 71% of the mobility gap, while restoring 1940 growth closes only 29%. But that is mostly labor earnings, and Piketty says labor-income inequality “has evidently little to do with r − g.”

7. Chris’s position: r > g is the risk premium

Chris: “I think I have come to a close that r > g, as this is what forces investment; the difference is possibly risk. We see wealth disappear not just via inheritance mechanisms, but also mal-investment. But a key point on why capital tends to beat wages is risk variance.”

This is a position, not a neutral summary, so it sits outside §§2–3. Three claims:

r > g is structural, not an accident. If capital earned no more than the economy grew, there would be no reward for deferring consumption and bearing loss, and nobody would invest. Growth theory agrees in its own terms: an economy with r < g has over-accumulated capital (it is “dynamically inefficient”), and Abel, Mankiw, Summers & Zeckhauser (1989) found the US economy dynamically efficient (verify). This is a stronger claim than Piketty’s “a historical fact, not a logical necessity.”
The gap is a risk premium. Wages are a low-variance claim; capital is a high-variance one, and r is its expected return. The sharpest support: safe rates have often run below g (Blanchard’s 2019 AEA address on public debt and low interest rates, verify), while risky returns run above it. If r > g holds for risky capital and fails for safe capital, the gap is priced risk. That ties to Risk and Entrepreneurship (profit is the reward for bearing risk correctly) and Variance Is Not Luck (variance is the neutral substrate; outcomes are what agents do with it).
Fortunes die by mal-investment, not just by inheritance. §3’s dissipation evidence counts spending and splitting among heirs. Chris adds losses: the high-variance claim pays off on average and destroys individual fortunes regularly.

What this reconciles. Read with (3), §5’s “do fortunes compound?” row stops being a contradiction. Aggregate r can exceed g while individual fortunes churn, because measured r averages over survivors and losers alike, while the top-wealth lists show only the survivors. Fagereng’s persistence and Summers’ Forbes churn are then both true: some families keep earning the premium, and many are wiped out by the variance. Concentration becomes a question about the dispersion of outcomes, not the mean of r.

What it leaves to the other side. A risk premium explains why r > g; it does not by itself say how concentrated the survivors become. And Fagereng’s finding that returns rise with wealth is not obviously risk: is that a higher premium for more risk, or scale advantages earning more for the same risk? That is the test question for this position.

Specimens

Tom Bilyeu × Economics Explained — inequality (2026-10) — the specimen that spawned this page. EE presents r > g as the “worse” case and Rognlie as the “better” one. Out of the discussion came Chris’s Chetty point (the 1940 cohort was measured in the r/g valley; §6 qualifies it), his concession on rates (§4 sizes it), and Tom’s “three generations” point (§3’s dissipation evidence).

Open Questions

Is Chetty’s mobility decline an r/g story at all? Chris’s original claim. The baseline problem stands (the 1940 cohort was measured from the valley), but the mechanism Chetty measured is the distribution of labor-earnings growth, which Piketty puts outside r − g. Does a channel connect them, for example through GLL’s labor-to-capital shift?
Rognlie vs. GLL: did non-housing capital gain share? Rognlie says the rise is all housing; GLL find 40% of equity growth from a labor→shareholder shift. Different measures and windows; the post-2000 corporate profit share is the lead (unverified). If it rose, the “it’s all housing” critique weakens. Cross-listed on Productivity–Pay Gap.
Risk or scale? (§7) Do larger fortunes earn more because they bear more risk (Chris’s premium story) or because scale earns more for the same risk (Piketty’s)? Fagereng et al. have risk-adjusted measures that may answer it.
Is net σ the crux? If one parameter decides whether the mechanism self-limits, what are Piketty–Zucman’s own estimates? (Not yet checked.)
Which top-share series do we trust? Saez–Zucman (22%) vs. Smith–Zidar–Zwick (15.7%). It’s the same pattern as the PSZ vs. Auten–Splinter income fight: the method choice is the result.
Housing: refutation or relocation? Rognlie reads “it’s all housing” against Piketty, and Piketty reads it as his multi-sector story. What drives the housing share is open. Chris leans macro (falling rates, global capital flows into housing as an asset) over local zoning, so positional goods is at most a partial account. A cross-country test would separate the two: does the housing share rise similarly in loosely and tightly zoned markets?

Sources

Piketty, Capital in the Twenty-First Century (Harvard UP, 2014): ch. 1 (first law), ch. 5 (second law), ch. 10 pp. 353–356 (chapter PDF), Table 12.2 pp. 448–449, ch. 15.
Piketty, “About Capital in the Twenty-First Century,” AER P&P 105(5):48–53 (2015). PDF
Saez & Zucman, “Wealth Inequality in the United States since 1913,” QJE 131(2):519–578 (2016). PDF
Smith, Zidar & Zwick, “Top Wealth in America,” QJE 138(1) (2023). link
Rognlie, “Deciphering the Fall and Rise in the Net Capital Share,” BPEA Spring 2015. PDF
Krusell & Smith, “Is Piketty’s ‘Second Law of Capitalism’ Fundamental?” JPE 123(4):725–748 (2015). PDF
Summers, “The Inequality Puzzle,” Democracy #32 (2014). PDF
Arnott, Bernstein & Wu, “The Rich Get Poorer,” Cato Journal 35(3) (2015), abstract level only. SSRN
Acemoglu & Robinson, “The Rise and Decline of General Laws of Capitalism,” JEP 29(1):3–28 (2015). link
Fagereng, Guiso, Malacrino & Pistaferri, “Heterogeneity and Persistence in Returns to Wealth,” Econometrica 88 (2020). NBER
Greenwald, Lettau & Ludvigson, “How the Wealth Was Won,” JPE 133(4) (2025). NBER
Gomez & Gouin-Bonenfant, Econometrica 92 (2024). DOI
Chetty et al., “The Fading American Dream,” Science 356(6336):398–406 (2017). NBER